Which interpretation do you prefer?
If I asssume a value of zero for the parameter, what is the probability of my observed parameter or more extreme?
Or
What’s the probability my result is greater than zero?
Which interpretation do you prefer?
If I repeat this study precisely an infinte number of times, and I calculate a 95% interval each time, then 95% of those intervals will contain the true parameter.
Or
What’s the probability the parameter falls in this interval?
Intuitive results
Auto-regularization
Guards against overfitting
Intervals for anything you can calculate
The goal is a distribution (stable) rather than a parameter
Posterior distribution
Represents our perspective regarding the intial state of affairs
Based on
Prior belief
Prior research
Known approaches that work well in the modeling context
(mpg ~ wt, data=mtcars)
(mpg ~ wt, data=mtcars)
(mpg ~ wt, data=mtcars)lm(mpg ~ wt, data=mtcars)
(mpg ~ wt, data=mtcars)
(mpg ~ wt, data=mtcars)lm(mpg ~ wt, data=mtcars)
stan_lm(mpg ~ wt, data=mtcars) # rstanarm
(mpg ~ wt, data=mtcars)lm(mpg ~ wt, data=mtcars)
stan_lm(mpg ~ wt, data=mtcars) # rstanarm
brm(mpg ~ wt, data=mtcars) # brmsglm(treat ~ educ + black + hisp + married, data=lalonde, family='binomial')
stan_glm(treat ~ educ + black + hisp + married, data=lalonde, family='binomial') # rstanarm
brm(treat ~ educ + black + hisp + married, data=lalonde, family='binomial') # brmsclm(rating ~ temp*contact, data = wine) # ordinal
stan_polr(rating ~ temp*contact, data = wine) # rstanarm
brm(rating ~ temp*contact, data = wine, family='ordinal') # brmslmer(Reaction ~ Days + (1 + Days|Subject)) # lme4
stan_lmer(Reaction ~ Days + (1 + Days|Subject)) # rstanarm
brm(Reaction ~ Days + (1 + Days|Subject)) # brms
Settings
Debugging
Diagnostics
Model comparison
Big data
Very complex models